This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##  [1] "re_yellow"      "pDSR_YE_ay"     "p_yellow"       "pDSR_YE_ayu"   
##  [5] "Hy_ay"          "pDSR_YE_ayg"    "Hy_ayg"         "pH"            
##  [9] "Hy_ayu"         "re_pelagic"     "beta1_pH"       "Hdnye_ay"      
## [13] "Hdnye_ayg"      "Tdnye_ayg"      "beta3_pH"       "Bdnye_ayg"     
## [17] "beta0_pH"       "mu_beta2_pH"    "beta2_pH"       "wt"            
## [21] "By_ay"          "By_ayg"         "Bb_ay"          "By_ayu"        
## [25] "Bb_ayg"         "Bb_ayu"         "Bp_ayu"         "Bp_ay"         
## [29] "Bs_ayu"         "mu_beta1_pH"    "Ro_ayu"         "Ro_ay"         
## [33] "Hd_ayg"         "p_dsr"          "Ho_ayu"         "Ry_ayu"        
## [37] "Ry_ayu_mort"    "Ho_ay"          "re_pH"          "Ry_ay"         
## [41] "Ry_ay_mort"     "Hd_ay"          "Tdnye_ay"       "Bdnye_ay"      
## [45] "Ro_ayg"         "Rb_ayu"         "Rb_ayu_mort"    "Rp_ayu"        
## [49] "Rp_ayu_mort"    "Rp_ay"          "Rp_ay_mort"     "Rb_ay_mort"    
## [53] "Rb_ay"          "Rs_ayg"         "Rs_ayg_mort"    "Rdnye_ayg"     
## [57] "Rdnye_ayg_mort" "Rd_ayg"         "Rs_ayu"         "Rs_ayu_mort"   
## [61] "Bs_ay"          "Ry_ayg"         "Ry_ayg_mort"    "R_ay"          
## [65] "R_ayu"          "Rdnye_ayu"      "Rdnye_ayu_mort" "Rb_ayg"        
## [69] "Rb_ayg_mort"    "R_ayg"          "Rp_ayg"         "Rp_ayg_mort"   
## [73] "Rdnye_ay"       "Rdnye_ay_mort"  "Rs_ay_mort"     "Rs_ay"         
## [77] "Ty_ayg"         "Hdnye_ayu"      "p_pelagic"      "Ty_ayu"        
## [81] "re_slope"       "re_rslope"      "H_ayu"          "Rd_ayu"        
## [85] "Rd_ay"          "H_ay"           "mu_beta0_pH"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_yellow 5 3.233032
beta0_yellow 5 3.114382
mu_beta0_yellow 1 1.969222
beta3_yellow 5 1.740860
beta1_pelagic 5 1.452666
beta3_pH 8 1.255894
beta2_pH 11 1.253673
tau_beta0_yellow 2 1.225658
beta1_pH 12 1.216402
parameter n badRhat_avg
beta2_yellow 4 1.212596
beta0_pelagic 5 1.202947
beta4_yellow 1 1.178759
beta3_pelagic 3 1.175361
beta0_pH 9 1.171366
beta2_pelagic 3 1.151014
beta4_pelagic 1 1.125283
mu_beta0_pH 1 1.111577
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta0_pH 0 0 1 0 0 0 0 0 0 0 0 2 1 3 0 2
beta0_pH 0 0 1 0 0 0 0 0 0 0 0 1 1 1 0 1
beta1_pH 0 0 1 1 1 1 0 0 0 0 1 2 1 2 1 1
beta1_pH 0 0 1 1 1 1 0 0 0 0 1 1 1 1 1 1
beta2_pH 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1
beta2_pH 0 1 1 1 0 1 1 0 0 0 1 1 1 1 1 1
beta3_pH 0 0 1 1 0 0 0 0 0 0 1 1 1 2 1 0
beta3_pH 0 0 1 1 0 0 0 0 0 0 1 1 1 1 1 0
Bp_ay 0 0 0 0 0 0 0 0 0 0 0 37 0 0 0 0
Bp_ayu 0 0 0 0 0 0 0 0 0 0 0 38 0 0 0 0
H_ay 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
H_ayu 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
Hd_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
Hd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
Hdnye_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
Hdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 2
Hdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
Ho_ay 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
Ho_ayu 0 0 0 0 2 0 0 0 2 0 0 0 0 0 0 0
Hy_ay 0 0 0 0 0 0 0 0 0 0 1 4 0 2 1 2
Hy_ayg 0 0 0 0 1 0 0 0 0 0 0 4 0 2 0 2
Hy_ayu 0 0 0 0 0 0 0 0 0 0 0 4 0 2 1 2
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta1_pH 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta2_pH 2 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
p_pelagic 0 0 0 10 0 0 0 0 0 0 13 0 0 0 0 0
p_yellow 0 0 0 0 0 0 0 0 0 0 3 8 0 6 1 6
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 2 4 0 4 1 3
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 1 4 0 3 0 3
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 2 4 0 3 1 3
pH 0 0 0 0 0 0 0 0 0 0 0 5 3 12 1 2
R_ay 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0
R_ayg 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 0
R_ayu 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
Rb_ay 0 0 0 0 0 1 3 0 0 0 0 1 4 11 0 0
Rb_ay_mort 0 0 0 0 0 1 3 0 0 0 0 1 4 11 0 0
Rb_ayg 0 0 1 0 1 0 4 0 0 0 0 0 0 0 0 1
Rb_ayg_mort 0 0 1 0 1 0 4 0 0 0 0 0 0 0 0 1
Rb_ayu 0 0 0 0 0 1 1 0 0 0 0 1 4 11 0 0
Rb_ayu_mort 0 0 0 0 0 1 1 0 0 0 0 1 4 11 0 0
Rd_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
Rd_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 0 2 0 5 0 2
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 0 2 0 5 0 2
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 1 1 8 0 2
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 1 1 8 0 2
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 1
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 2 0 3 0 1
re_pelagic 0 0 0 0 0 0 0 0 0 0 32 0 0 0 0 16
re_pH 0 0 19 0 0 0 0 0 0 0 13 22 19 26 10 15
re_rslope 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
re_slope 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
Ro_ay 0 0 0 0 11 16 0 2 0 1 0 2 0 4 0 2
Ro_ayg 0 0 0 0 1 2 0 1 0 0 0 1 2 8 0 2
Ro_ayu 0 0 0 1 12 16 0 2 0 1 0 2 0 3 0 1
Rp_ay 0 0 0 0 0 1 3 0 0 0 0 1 4 11 0 0
Rp_ay_mort 0 0 0 0 0 1 3 0 0 0 0 1 4 11 0 0
Rp_ayg 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 1
Rp_ayg_mort 0 0 0 0 1 0 4 0 0 0 0 0 0 0 0 1
Rp_ayu 0 0 0 0 0 1 1 0 0 0 0 1 4 11 0 0
Rp_ayu_mort 0 0 0 0 0 1 1 0 0 0 0 1 4 11 0 0
Rs_ay 0 0 0 0 0 0 0 0 0 0 0 3 0 4 0 2
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 0 3 0 4 0 2
Rs_ayg 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 2
Rs_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 1 0 4 0 2
Rs_ayu 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 1
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 4 0 1 0 1
Ry_ay 0 0 0 0 13 1 0 1 1 0 0 0 0 0 0 1
Ry_ay_mort 0 0 0 0 13 1 0 1 1 0 0 0 0 0 0 1
Ry_ayg 0 0 0 0 3 0 1 0 0 1 0 0 0 0 0 0
Ry_ayg_mort 0 0 0 0 3 0 1 0 0 1 0 0 0 0 0 0
Ry_ayu 0 0 0 2 13 2 0 2 1 0 0 0 0 0 0 1
Ry_ayu_mort 0 0 0 2 13 2 0 2 1 0 0 0 0 0 0 1
beta0_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1
beta0_yellow 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1
beta1_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 1 0 1
beta1_yellow 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1
beta2_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 0
beta2_yellow 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0
beta3_pelagic 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 0
beta3_yellow 0 0 0 0 0 0 0 0 0 0 1 1 0 1 1 1
beta4_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
beta4_yellow 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
mu_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.129 0.072 -0.263 -0.134 0.022
mu_bc_H[2] -0.101 0.044 -0.177 -0.105 -0.004
mu_bc_H[3] -0.439 0.067 -0.566 -0.440 -0.308
mu_bc_H[4] -0.999 0.196 -1.409 -0.995 -0.628
mu_bc_H[5] 0.920 0.950 -0.152 0.711 3.374
mu_bc_H[6] -2.197 0.322 -2.817 -2.201 -1.536
mu_bc_H[7] -0.456 0.109 -0.677 -0.455 -0.248
mu_bc_H[8] 0.250 0.363 -0.344 0.210 1.068
mu_bc_H[9] -0.298 0.131 -0.551 -0.300 -0.038
mu_bc_H[10] -0.101 0.072 -0.234 -0.103 0.046
mu_bc_H[11] -0.125 0.038 -0.197 -0.126 -0.050
mu_bc_H[12] -0.254 0.106 -0.484 -0.250 -0.053
mu_bc_H[13] -0.154 0.081 -0.310 -0.153 0.002
mu_bc_H[14] -0.305 0.100 -0.502 -0.303 -0.114
mu_bc_H[15] -0.341 0.050 -0.442 -0.341 -0.241
mu_bc_H[16] -0.301 0.377 -0.973 -0.323 0.512
mu_bc_R[1] 1.325 0.139 1.050 1.321 1.602
mu_bc_R[2] 1.458 0.095 1.268 1.458 1.638
mu_bc_R[3] 1.401 0.142 1.124 1.403 1.674
mu_bc_R[4] 0.928 0.205 0.500 0.936 1.308
mu_bc_R[5] 1.227 0.464 0.296 1.244 2.129
mu_bc_R[6] -1.583 0.419 -2.414 -1.580 -0.772
mu_bc_R[7] 0.452 0.203 0.029 0.460 0.843
mu_bc_R[8] 0.537 0.185 0.166 0.543 0.892
mu_bc_R[9] 0.338 0.205 -0.095 0.349 0.699
mu_bc_R[10] 1.314 0.168 0.974 1.322 1.635
mu_bc_R[11] 1.045 0.101 0.847 1.045 1.237
mu_bc_R[12] 0.822 0.205 0.415 0.829 1.215
mu_bc_R[13] 1.030 0.104 0.822 1.031 1.227
mu_bc_R[14] 0.900 0.143 0.615 0.901 1.169
mu_bc_R[15] 0.788 0.111 0.566 0.792 1.006
mu_bc_R[16] 1.100 0.131 0.837 1.100 1.361
tau_pH[1] 4.721 1.109 0.882 5.001 6.030
tau_pH[2] 1.984 0.226 1.562 1.975 2.449
tau_pH[3] 2.113 0.242 1.622 2.112 2.592
beta0_pH[1,1] 0.611 0.284 0.174 0.580 1.476
beta0_pH[2,1] 1.449 0.354 0.948 1.393 2.594
beta0_pH[3,1] 1.592 0.421 1.008 1.495 2.603
beta0_pH[4,1] 1.678 0.349 1.168 1.634 2.804
beta0_pH[5,1] -0.772 0.454 -1.518 -0.807 0.682
beta0_pH[6,1] -0.634 0.572 -2.179 -0.582 0.619
beta0_pH[7,1] -0.475 0.487 -1.434 -0.475 0.809
beta0_pH[8,1] -0.604 0.396 -1.375 -0.609 0.493
beta0_pH[9,1] -0.526 0.357 -1.069 -0.570 0.522
beta0_pH[10,1] 0.422 0.277 -0.013 0.393 1.246
beta0_pH[11,1] 0.068 0.523 -0.450 -0.050 1.932
beta0_pH[12,1] 0.554 0.360 0.102 0.502 1.907
beta0_pH[13,1] 0.115 0.440 -0.274 0.025 1.767
beta0_pH[14,1] -0.207 0.417 -0.628 -0.287 1.503
beta0_pH[15,1] 0.036 0.394 -0.447 -0.036 1.453
beta0_pH[16,1] -0.327 0.570 -1.121 -0.394 1.788
beta0_pH[1,2] 2.835 0.161 2.503 2.844 3.136
beta0_pH[2,2] 2.889 0.133 2.616 2.892 3.141
beta0_pH[3,2] 3.131 0.150 2.845 3.126 3.443
beta0_pH[4,2] 2.950 0.133 2.687 2.949 3.212
beta0_pH[5,2] 4.777 1.409 3.021 4.471 8.608
beta0_pH[6,2] 3.114 0.212 2.685 3.114 3.531
beta0_pH[7,2] 1.836 0.198 1.448 1.840 2.224
beta0_pH[8,2] 2.872 0.175 2.532 2.873 3.210
beta0_pH[9,2] 3.431 0.221 3.005 3.431 3.869
beta0_pH[10,2] 3.699 0.209 3.305 3.696 4.117
beta0_pH[11,2] -4.838 0.312 -5.493 -4.826 -4.234
beta0_pH[12,2] -4.605 0.433 -5.453 -4.600 -3.744
beta0_pH[13,2] -4.502 0.397 -5.255 -4.516 -3.687
beta0_pH[14,2] -5.506 0.475 -6.507 -5.490 -4.631
beta0_pH[15,2] -4.245 0.344 -4.882 -4.247 -3.573
beta0_pH[16,2] -4.764 0.420 -5.632 -4.740 -3.967
beta0_pH[1,3] -0.110 0.708 -1.755 -0.022 1.033
beta0_pH[2,3] 2.192 0.161 1.888 2.188 2.506
beta0_pH[3,3] 2.531 0.156 2.221 2.530 2.830
beta0_pH[4,3] 2.966 0.160 2.640 2.968 3.272
beta0_pH[5,3] 2.144 1.399 0.382 1.850 5.924
beta0_pH[6,3] 0.994 0.484 -0.176 1.020 1.863
beta0_pH[7,3] 0.630 0.173 0.293 0.628 0.974
beta0_pH[8,3] 0.310 0.191 -0.074 0.312 0.682
beta0_pH[9,3] -0.634 0.409 -1.776 -0.589 0.035
beta0_pH[10,3] 0.467 0.382 -0.488 0.519 1.071
beta0_pH[11,3] -0.179 0.354 -0.844 -0.193 0.519
beta0_pH[12,3] -0.874 0.367 -1.692 -0.851 -0.237
beta0_pH[13,3] -0.131 0.373 -0.897 -0.141 0.634
beta0_pH[14,3] -0.233 0.406 -0.871 -0.265 1.041
beta0_pH[15,3] -0.612 0.292 -1.244 -0.601 -0.091
beta0_pH[16,3] -0.361 0.301 -0.924 -0.363 0.212
beta1_pH[1,1] 2.983 0.577 1.299 3.044 3.914
beta1_pH[2,1] 2.047 0.556 0.120 2.101 2.889
beta1_pH[3,1] 1.758 0.671 0.005 1.877 2.712
beta1_pH[4,1] 2.242 0.621 0.021 2.304 3.255
beta1_pH[5,1] 2.210 0.519 0.666 2.231 3.137
beta1_pH[6,1] 3.513 1.295 0.485 3.374 6.386
beta1_pH[7,1] 2.585 0.938 0.048 2.588 4.486
beta1_pH[8,1] 3.587 1.219 0.075 3.515 6.375
beta1_pH[9,1] 2.160 0.505 0.701 2.216 2.920
beta1_pH[10,1] 2.102 0.479 0.074 2.165 2.749
beta1_pH[11,1] 3.072 0.662 0.003 3.209 3.709
beta1_pH[12,1] 2.474 0.537 0.002 2.538 3.061
beta1_pH[13,1] 2.848 0.589 0.001 2.963 3.429
beta1_pH[14,1] 3.268 0.636 0.008 3.387 3.855
beta1_pH[15,1] 2.447 0.528 0.003 2.533 3.043
beta1_pH[16,1] 3.903 0.925 0.005 4.003 5.325
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.011 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.015 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.660 0.346 5.997 6.645 7.397
beta1_pH[12,2] 6.290 0.491 5.336 6.282 7.272
beta1_pH[13,2] 6.884 0.436 6.001 6.891 7.737
beta1_pH[14,2] 7.152 0.490 6.265 7.151 8.147
beta1_pH[15,2] 6.719 0.372 5.992 6.718 7.478
beta1_pH[16,2] 7.351 0.461 6.469 7.341 8.326
beta1_pH[1,3] 4.596 1.629 2.121 4.320 8.053
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 4.281 6.618 0.741 2.863 20.292
beta1_pH[6,3] 12.598 31.598 0.458 2.732 129.431
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.738 0.352 2.056 2.733 3.429
beta1_pH[9,3] 2.765 0.481 2.011 2.705 4.060
beta1_pH[10,3] 2.906 0.458 2.148 2.857 4.028
beta1_pH[11,3] 2.785 0.417 1.960 2.790 3.598
beta1_pH[12,3] 4.120 0.464 3.270 4.104 5.059
beta1_pH[13,3] 1.700 0.407 0.835 1.716 2.499
beta1_pH[14,3] 2.455 0.558 0.458 2.503 3.257
beta1_pH[15,3] 1.912 0.315 1.295 1.907 2.522
beta1_pH[16,3] 1.760 0.338 1.086 1.771 2.382
beta2_pH[1,1] 0.749 1.935 0.266 0.465 6.720
beta2_pH[2,1] 1.312 2.845 0.214 0.551 11.658
beta2_pH[3,1] 0.803 2.347 -2.239 0.560 8.199
beta2_pH[4,1] 0.878 2.307 0.187 0.458 8.060
beta2_pH[5,1] 1.421 1.043 0.182 1.296 3.899
beta2_pH[6,1] 0.244 0.430 0.079 0.183 0.843
beta2_pH[7,1] 0.013 0.063 0.000 0.000 0.053
beta2_pH[8,1] 0.280 0.488 0.114 0.240 0.729
beta2_pH[9,1] 0.490 0.583 0.174 0.411 1.416
beta2_pH[10,1] 0.628 0.500 0.241 0.559 1.409
beta2_pH[11,1] 0.663 1.727 0.416 0.773 1.639
beta2_pH[12,1] 1.153 1.796 0.075 1.240 2.802
beta2_pH[13,1] 0.571 1.725 0.351 0.696 1.391
beta2_pH[14,1] 0.683 1.665 0.418 0.806 1.606
beta2_pH[15,1] 0.627 1.753 0.190 0.725 1.855
beta2_pH[16,1] 0.223 1.766 0.155 0.327 1.135
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -1.948 1.847 -7.046 -1.455 -0.026
beta2_pH[4,2] -1.795 1.687 -6.337 -1.313 -0.026
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.797 4.504 -21.056 -8.799 -4.024
beta2_pH[12,2] -7.969 5.393 -20.922 -7.204 -0.708
beta2_pH[13,2] -8.136 5.115 -20.343 -7.218 -1.718
beta2_pH[14,2] -8.869 4.720 -20.665 -7.996 -2.645
beta2_pH[15,2] -9.586 4.502 -20.729 -8.603 -3.725
beta2_pH[16,2] -9.804 4.406 -21.068 -8.798 -4.011
beta2_pH[1,3] 0.239 0.226 0.101 0.184 0.681
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 8.967 6.247 -0.227 8.200 23.020
beta2_pH[6,3] 9.153 6.124 0.235 8.284 23.453
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.065 5.629 2.022 9.041 23.587
beta2_pH[9,3] 8.897 6.216 0.464 7.895 23.519
beta2_pH[10,3] 8.564 6.425 0.486 7.560 23.446
beta2_pH[11,3] -2.119 1.627 -6.918 -1.652 -0.587
beta2_pH[12,3] -2.206 1.395 -6.028 -1.797 -0.906
beta2_pH[13,3] -2.344 2.141 -8.134 -1.954 1.434
beta2_pH[14,3] -2.233 1.732 -6.582 -1.907 1.849
beta2_pH[15,3] -2.672 1.717 -7.627 -2.153 -0.963
beta2_pH[16,3] -2.755 1.929 -8.321 -2.122 -0.874
beta3_pH[1,1] 35.960 1.381 33.533 35.976 38.112
beta3_pH[2,1] 33.618 2.104 30.415 33.549 37.664
beta3_pH[3,1] 32.335 4.217 18.803 33.432 35.990
beta3_pH[4,1] 33.555 2.923 22.034 33.898 37.249
beta3_pH[5,1] 27.936 2.059 26.106 27.502 33.563
beta3_pH[6,1] 37.629 3.626 30.051 37.607 44.760
beta3_pH[7,1] 30.904 7.931 18.610 30.623 45.019
beta3_pH[8,1] 38.763 3.220 32.202 38.808 44.633
beta3_pH[9,1] 30.826 1.973 28.057 30.723 34.660
beta3_pH[10,1] 32.954 1.841 30.718 32.976 35.501
beta3_pH[11,1] 30.860 2.407 29.499 30.323 40.428
beta3_pH[12,1] 30.655 2.166 29.293 30.186 38.464
beta3_pH[13,1] 33.596 1.727 32.152 33.278 40.187
beta3_pH[14,1] 32.217 1.202 31.118 32.051 34.744
beta3_pH[15,1] 31.346 1.360 29.641 31.175 34.416
beta3_pH[16,1] 32.297 1.406 30.422 32.070 36.279
beta3_pH[1,2] 30.006 7.947 18.476 28.919 44.837
beta3_pH[2,2] 30.127 7.905 18.496 29.317 44.890
beta3_pH[3,2] 29.695 7.883 18.499 28.749 44.701
beta3_pH[4,2] 30.034 7.968 18.524 29.206 44.960
beta3_pH[5,2] 29.921 7.933 18.448 28.978 44.808
beta3_pH[6,2] 29.920 7.965 18.516 28.957 45.116
beta3_pH[7,2] 30.002 7.905 18.508 29.203 44.883
beta3_pH[8,2] 30.023 7.957 18.505 29.046 44.874
beta3_pH[9,2] 30.025 8.012 18.343 29.037 44.930
beta3_pH[10,2] 29.906 7.909 18.365 28.869 45.016
beta3_pH[11,2] 43.418 0.178 43.123 43.403 43.782
beta3_pH[12,2] 43.185 0.227 42.784 43.138 43.762
beta3_pH[13,2] 43.856 0.159 43.409 43.904 44.034
beta3_pH[14,2] 43.293 0.199 43.049 43.237 43.778
beta3_pH[15,2] 43.405 0.195 43.106 43.381 43.804
beta3_pH[16,2] 43.488 0.187 43.150 43.487 43.836
beta3_pH[1,3] 39.084 3.223 33.072 38.965 45.398
beta3_pH[2,3] 30.032 8.004 18.417 29.229 44.916
beta3_pH[3,3] 30.014 7.903 18.394 29.225 44.786
beta3_pH[4,3] 30.119 7.971 18.514 29.050 44.916
beta3_pH[5,3] 36.874 3.863 31.304 36.311 44.925
beta3_pH[6,3] 40.440 3.495 31.758 40.774 45.603
beta3_pH[7,3] 38.029 4.320 31.311 37.731 45.521
beta3_pH[8,3] 41.490 0.246 41.063 41.492 41.926
beta3_pH[9,3] 33.473 0.597 31.592 33.566 34.301
beta3_pH[10,3] 35.829 0.805 33.457 36.012 36.860
beta3_pH[11,3] 41.669 0.817 40.030 41.695 43.199
beta3_pH[12,3] 41.758 0.400 40.985 41.760 42.531
beta3_pH[13,3] 42.352 2.555 31.104 42.766 45.046
beta3_pH[14,3] 40.741 2.048 30.877 41.080 42.346
beta3_pH[15,3] 42.370 0.691 40.887 42.426 43.542
beta3_pH[16,3] 42.854 0.837 41.086 42.977 44.147
beta0_pelagic[1] 2.222 0.132 1.960 2.223 2.477
beta0_pelagic[2] 1.498 0.127 1.250 1.505 1.743
beta0_pelagic[3] -0.312 0.767 -2.226 -0.051 0.629
beta0_pelagic[4] -0.317 0.735 -1.756 -0.205 0.779
beta0_pelagic[5] 1.197 0.266 0.643 1.198 1.719
beta0_pelagic[6] 1.468 0.270 0.898 1.482 1.982
beta0_pelagic[7] 1.605 0.220 1.189 1.593 2.077
beta0_pelagic[8] 1.758 0.199 1.390 1.756 2.167
beta0_pelagic[9] 2.451 0.307 1.847 2.452 3.018
beta0_pelagic[10] 2.481 0.209 2.013 2.499 2.849
beta0_pelagic[11] 0.019 0.491 -1.053 0.037 0.705
beta0_pelagic[12] 1.677 0.146 1.388 1.678 1.968
beta0_pelagic[13] 0.352 0.182 -0.033 0.356 0.687
beta0_pelagic[14] -0.090 0.317 -0.790 -0.054 0.401
beta0_pelagic[15] -0.267 0.137 -0.542 -0.263 0.011
beta0_pelagic[16] 0.301 0.255 -0.208 0.339 0.656
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.663 1.096 0.441 1.271 4.353
beta1_pelagic[4] 1.660 0.904 0.442 1.476 3.928
beta1_pelagic[5] -0.072 0.322 -0.689 -0.076 0.563
beta1_pelagic[6] -0.090 0.455 -0.855 -0.130 0.744
beta1_pelagic[7] -0.028 0.304 -0.617 -0.023 0.567
beta1_pelagic[8] -0.010 0.278 -0.562 -0.016 0.553
beta1_pelagic[9] 0.248 0.482 -0.746 0.362 0.991
beta1_pelagic[10] 0.093 0.271 -0.444 0.083 0.646
beta1_pelagic[11] 3.890 1.264 2.292 3.565 6.001
beta1_pelagic[12] 2.784 0.316 2.196 2.779 3.425
beta1_pelagic[13] 2.721 0.610 1.701 2.693 4.050
beta1_pelagic[14] 4.213 1.146 2.730 3.927 7.171
beta1_pelagic[15] 2.916 0.247 2.432 2.930 3.369
beta1_pelagic[16] 3.493 0.771 2.625 3.272 5.977
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 1.049 2.808 0.043 0.213 9.641
beta2_pelagic[4] 1.531 3.442 0.039 0.377 13.374
beta2_pelagic[5] -0.005 0.656 -1.398 -0.001 1.370
beta2_pelagic[6] -0.091 0.693 -1.546 -0.141 1.365
beta2_pelagic[7] 0.023 0.654 -1.292 0.024 1.415
beta2_pelagic[8] -0.002 0.659 -1.322 -0.006 1.381
beta2_pelagic[9] 0.247 0.677 -1.174 0.286 1.599
beta2_pelagic[10] -0.003 0.647 -1.564 0.039 1.201
beta2_pelagic[11] 1.999 3.506 0.113 0.232 11.814
beta2_pelagic[12] 6.173 5.157 0.987 4.672 20.190
beta2_pelagic[13] 1.335 2.761 0.222 0.550 8.980
beta2_pelagic[14] 0.353 0.224 0.157 0.307 0.809
beta2_pelagic[15] 6.285 4.837 1.147 5.005 19.363
beta2_pelagic[16] 5.359 5.669 0.219 3.998 20.985
beta3_pelagic[1] 29.889 7.845 18.406 29.152 44.827
beta3_pelagic[2] 30.005 7.810 18.586 29.250 44.743
beta3_pelagic[3] 28.403 5.539 18.641 28.478 41.870
beta3_pelagic[4] 24.443 4.136 18.578 24.051 35.731
beta3_pelagic[5] 30.041 8.158 18.498 28.649 45.251
beta3_pelagic[6] 31.790 6.910 18.932 31.600 44.412
beta3_pelagic[7] 29.347 7.910 18.297 28.158 44.673
beta3_pelagic[8] 29.921 7.969 18.463 28.675 45.032
beta3_pelagic[9] 30.809 6.115 19.100 30.761 43.172
beta3_pelagic[10] 29.384 8.229 18.423 27.902 45.101
beta3_pelagic[11] 42.590 2.460 34.844 43.112 45.629
beta3_pelagic[12] 43.462 0.277 42.985 43.455 43.965
beta3_pelagic[13] 42.682 1.267 40.098 42.690 45.261
beta3_pelagic[14] 42.198 1.618 39.061 42.178 45.484
beta3_pelagic[15] 43.148 0.274 42.442 43.155 43.664
beta3_pelagic[16] 43.096 0.735 41.081 43.233 44.333
mu_beta0_pelagic[1] 0.721 1.041 -1.493 0.804 2.773
mu_beta0_pelagic[2] 1.798 0.382 0.991 1.810 2.556
mu_beta0_pelagic[3] 0.334 0.456 -0.575 0.346 1.206
tau_beta0_pelagic[1] 0.519 0.596 0.049 0.318 2.127
tau_beta0_pelagic[2] 2.998 3.264 0.289 2.087 11.747
tau_beta0_pelagic[3] 1.560 1.147 0.208 1.288 4.526
beta0_yellow[1] -0.545 0.214 -1.063 -0.526 -0.203
beta0_yellow[2] 0.455 0.206 -0.059 0.474 0.763
beta0_yellow[3] -0.350 0.207 -0.836 -0.336 0.013
beta0_yellow[4] 0.776 0.292 -0.058 0.829 1.192
beta0_yellow[5] -0.289 0.351 -0.956 -0.287 0.395
beta0_yellow[6] 1.117 0.171 0.771 1.119 1.455
beta0_yellow[7] 0.979 0.158 0.664 0.978 1.284
beta0_yellow[8] 1.008 0.156 0.709 1.009 1.308
beta0_yellow[9] 0.659 0.159 0.354 0.657 0.974
beta0_yellow[10] 0.593 0.144 0.308 0.595 0.869
beta0_yellow[11] -1.678 0.660 -2.906 -1.721 -0.202
beta0_yellow[12] -3.022 0.952 -4.436 -3.350 -1.503
beta0_yellow[13] -3.570 0.427 -4.445 -3.576 -2.704
beta0_yellow[14] -1.587 0.948 -2.971 -1.890 0.047
beta0_yellow[15] -2.472 0.601 -3.380 -2.598 -1.119
beta0_yellow[16] -1.983 0.859 -3.080 -2.253 -0.237
beta1_yellow[1] 0.841 0.988 0.006 0.675 2.829
beta1_yellow[2] 1.160 0.480 0.605 1.078 2.385
beta1_yellow[3] 0.771 0.307 0.262 0.739 1.497
beta1_yellow[4] 1.579 0.924 0.676 1.276 4.476
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 1.815 0.685 0.282 1.869 3.070
beta1_yellow[12] 1.706 1.087 0.103 2.149 3.247
beta1_yellow[13] 2.683 0.421 1.765 2.686 3.537
beta1_yellow[14] 1.678 0.922 0.009 1.951 3.044
beta1_yellow[15] 1.693 0.638 0.241 1.850 2.580
beta1_yellow[16] 1.724 0.872 0.006 2.010 2.792
beta2_yellow[1] -2.081 2.166 -7.977 -1.364 0.018
beta2_yellow[2] -1.955 2.023 -7.966 -1.297 -0.130
beta2_yellow[3] -1.576 1.515 -5.589 -1.051 -0.110
beta2_yellow[4] -1.604 1.935 -6.814 -0.773 -0.085
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -5.028 3.069 -12.989 -4.312 -1.138
beta2_yellow[12] -5.215 2.946 -11.961 -4.563 -1.149
beta2_yellow[13] -5.120 2.898 -12.303 -4.380 -1.490
beta2_yellow[14] -5.123 3.129 -13.022 -4.529 -0.526
beta2_yellow[15] -4.890 2.936 -11.891 -4.266 -0.983
beta2_yellow[16] -5.248 3.008 -12.570 -4.639 -1.099
beta3_yellow[1] 25.911 7.209 18.244 22.959 44.158
beta3_yellow[2] 29.241 2.288 24.187 29.084 33.904
beta3_yellow[3] 32.961 3.608 24.528 32.910 40.992
beta3_yellow[4] 28.788 3.864 19.675 28.200 35.745
beta3_yellow[5] 30.290 7.964 18.513 29.589 44.947
beta3_yellow[6] 30.215 8.002 18.562 29.290 44.964
beta3_yellow[7] 29.973 7.889 18.500 29.104 44.761
beta3_yellow[8] 30.165 7.898 18.503 29.369 44.831
beta3_yellow[9] 30.189 7.970 18.517 29.186 44.994
beta3_yellow[10] 29.965 7.919 18.487 28.927 44.862
beta3_yellow[11] 45.013 1.211 42.575 45.276 45.967
beta3_yellow[12] 42.190 2.455 34.674 43.127 44.314
beta3_yellow[13] 44.827 0.438 43.883 44.914 45.576
beta3_yellow[14] 42.247 3.855 33.460 43.977 45.787
beta3_yellow[15] 44.556 1.806 37.313 44.923 45.949
beta3_yellow[16] 43.702 2.529 34.853 44.390 45.804
mu_beta0_yellow[1] 0.048 0.541 -1.102 0.062 1.145
mu_beta0_yellow[2] 0.653 0.334 -0.106 0.675 1.295
mu_beta0_yellow[3] -2.087 0.817 -3.289 -2.248 -0.347
tau_beta0_yellow[1] 2.238 4.650 0.103 1.237 9.022
tau_beta0_yellow[2] 3.610 4.515 0.306 2.424 13.723
tau_beta0_yellow[3] 1.434 2.930 0.103 0.798 6.512
beta0_black[1] -0.071 0.161 -0.393 -0.072 0.246
beta0_black[2] 1.917 0.127 1.668 1.917 2.163
beta0_black[3] 1.320 0.134 1.063 1.318 1.587
beta0_black[4] 2.430 0.135 2.169 2.428 2.707
beta0_black[5] 4.726 2.172 1.831 4.278 10.379
beta0_black[6] 4.689 1.958 2.301 4.207 9.867
beta0_black[7] 3.770 1.825 1.584 3.282 8.549
beta0_black[8] 0.950 0.214 0.553 0.944 1.385
beta0_black[9] 2.614 0.234 2.154 2.614 3.055
beta0_black[10] 1.461 0.137 1.205 1.461 1.727
beta0_black[11] 3.480 0.152 3.179 3.483 3.768
beta0_black[12] 4.869 0.177 4.519 4.866 5.220
beta0_black[13] -0.121 0.244 -0.612 -0.117 0.331
beta0_black[14] 2.854 0.160 2.546 2.853 3.168
beta0_black[15] 1.289 0.156 0.990 1.289 1.594
beta0_black[16] 4.274 0.164 3.964 4.272 4.593
beta2_black[1] 7.334 9.636 0.561 3.267 39.043
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -2.193 1.780 -7.241 -1.666 -0.437
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.774 1.051 39.876 41.898 43.324
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.296 0.759 37.602 39.369 40.577
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.266 0.195 -0.647 -0.264 0.107
beta4_black[2] 0.241 0.184 -0.130 0.242 0.600
beta4_black[3] -0.936 0.193 -1.305 -0.944 -0.536
beta4_black[4] 0.425 0.219 0.007 0.423 0.866
beta4_black[5] 0.582 1.377 -1.392 0.364 3.845
beta4_black[6] 0.516 1.239 -1.298 0.316 3.532
beta4_black[7] 0.439 1.320 -1.328 0.241 3.274
beta4_black[8] -0.236 0.325 -0.879 -0.229 0.374
beta4_black[9] 0.829 0.776 -0.300 0.682 2.704
beta4_black[10] 0.053 0.191 -0.321 0.053 0.427
beta4_black[11] -0.688 0.215 -1.108 -0.685 -0.274
beta4_black[12] 0.175 0.323 -0.435 0.165 0.831
beta4_black[13] -1.181 0.228 -1.634 -1.181 -0.747
beta4_black[14] -0.179 0.237 -0.624 -0.179 0.288
beta4_black[15] -0.878 0.216 -1.314 -0.877 -0.454
beta4_black[16] -0.593 0.231 -1.050 -0.593 -0.129
mu_beta0_black[1] 1.291 0.894 -0.673 1.316 3.014
mu_beta0_black[2] 2.704 1.070 0.749 2.622 5.105
mu_beta0_black[3] 2.532 0.979 0.445 2.556 4.406
tau_beta0_black[1] 0.666 0.655 0.056 0.464 2.328
tau_beta0_black[2] 0.433 0.638 0.045 0.233 2.050
tau_beta0_black[3] 0.238 0.161 0.050 0.201 0.633
beta0_dsr[11] -2.866 0.295 -3.421 -2.862 -2.308
beta0_dsr[12] 4.557 0.281 4.028 4.554 5.116
beta0_dsr[13] -1.360 0.297 -1.950 -1.355 -0.798
beta0_dsr[14] -3.777 0.531 -4.865 -3.784 -2.740
beta0_dsr[15] -1.961 0.276 -2.512 -1.960 -1.418
beta0_dsr[16] -3.036 0.383 -3.809 -3.035 -2.304
beta1_dsr[11] 4.807 0.314 4.222 4.801 5.436
beta1_dsr[12] 6.538 6.628 2.254 5.042 20.572
beta1_dsr[13] 2.862 0.308 2.269 2.856 3.469
beta1_dsr[14] 6.442 0.555 5.374 6.434 7.556
beta1_dsr[15] 3.365 0.286 2.789 3.371 3.913
beta1_dsr[16] 5.845 0.395 5.112 5.835 6.661
beta2_dsr[11] -8.917 2.626 -13.806 -8.645 -4.566
beta2_dsr[12] -7.378 2.835 -13.459 -7.161 -2.446
beta2_dsr[13] -6.777 2.860 -12.909 -6.578 -1.840
beta2_dsr[14] -6.440 2.836 -12.592 -6.266 -1.921
beta2_dsr[15] -8.080 2.631 -14.033 -7.753 -3.941
beta2_dsr[16] -8.232 2.482 -13.913 -7.951 -4.339
beta3_dsr[11] 43.486 0.157 43.203 43.482 43.786
beta3_dsr[12] 33.969 0.728 32.081 34.131 34.820
beta3_dsr[13] 43.255 0.273 42.837 43.190 43.858
beta3_dsr[14] 43.334 0.219 43.073 43.269 43.867
beta3_dsr[15] 43.514 0.190 43.168 43.512 43.862
beta3_dsr[16] 43.439 0.163 43.164 43.426 43.763
beta4_dsr[11] 0.580 0.215 0.169 0.576 1.002
beta4_dsr[12] 0.256 0.435 -0.580 0.251 1.153
beta4_dsr[13] -0.156 0.225 -0.606 -0.159 0.289
beta4_dsr[14] 0.149 0.254 -0.352 0.153 0.627
beta4_dsr[15] 0.719 0.214 0.323 0.713 1.129
beta4_dsr[16] 0.167 0.232 -0.270 0.168 0.630
beta0_slope[11] -1.845 0.148 -2.139 -1.841 -1.555
beta0_slope[12] -4.461 0.254 -4.979 -4.457 -3.989
beta0_slope[13] -1.360 0.191 -1.814 -1.343 -1.047
beta0_slope[14] -2.680 0.164 -3.000 -2.682 -2.363
beta0_slope[15] -1.338 0.151 -1.632 -1.338 -1.042
beta0_slope[16] -2.729 0.162 -3.039 -2.730 -2.411
beta1_slope[11] 4.488 0.222 4.066 4.487 4.926
beta1_slope[12] 4.021 0.450 3.180 4.013 4.956
beta1_slope[13] 2.754 0.488 2.200 2.666 4.235
beta1_slope[14] 6.323 0.423 5.484 6.318 7.159
beta1_slope[15] 3.007 0.208 2.588 3.008 3.398
beta1_slope[16] 5.286 0.291 4.714 5.287 5.879
beta2_slope[11] 8.438 1.974 5.201 8.294 12.521
beta2_slope[12] 6.652 2.857 1.203 6.669 12.627
beta2_slope[13] 5.187 3.052 0.360 5.142 11.511
beta2_slope[14] 6.271 2.517 2.199 6.074 11.627
beta2_slope[15] 8.226 2.398 4.556 7.820 13.740
beta2_slope[16] 7.772 2.267 4.353 7.413 13.104
beta3_slope[11] 43.461 0.133 43.226 43.459 43.719
beta3_slope[12] 43.351 0.275 42.904 43.319 43.899
beta3_slope[13] 43.456 0.421 42.871 43.386 44.136
beta3_slope[14] 43.272 0.137 43.096 43.240 43.616
beta3_slope[15] 43.497 0.162 43.199 43.497 43.795
beta3_slope[16] 43.372 0.142 43.151 43.350 43.698
beta4_slope[11] -0.736 0.165 -1.066 -0.738 -0.407
beta4_slope[12] -1.192 0.466 -2.216 -1.161 -0.406
beta4_slope[13] 0.090 0.161 -0.232 0.087 0.403
beta4_slope[14] -0.089 0.200 -0.479 -0.090 0.314
beta4_slope[15] -0.766 0.161 -1.074 -0.769 -0.451
beta4_slope[16] -0.164 0.175 -0.510 -0.163 0.179
sigma_H[1] 0.198 0.057 0.090 0.195 0.312
sigma_H[2] 0.171 0.030 0.118 0.168 0.237
sigma_H[3] 0.198 0.043 0.121 0.195 0.289
sigma_H[4] 0.420 0.077 0.297 0.411 0.594
sigma_H[5] 0.986 0.210 0.608 0.979 1.418
sigma_H[6] 0.409 0.195 0.050 0.400 0.808
sigma_H[7] 0.310 0.064 0.210 0.300 0.459
sigma_H[8] 0.416 0.091 0.281 0.405 0.615
sigma_H[9] 0.522 0.124 0.322 0.507 0.814
sigma_H[10] 0.210 0.043 0.135 0.206 0.305
sigma_H[11] 0.278 0.046 0.200 0.274 0.377
sigma_H[12] 0.439 0.166 0.209 0.419 0.777
sigma_H[13] 0.214 0.039 0.146 0.211 0.297
sigma_H[14] 0.507 0.094 0.348 0.502 0.705
sigma_H[15] 0.247 0.040 0.179 0.242 0.335
sigma_H[16] 0.227 0.045 0.154 0.223 0.330
lambda_H[1] 3.232 4.355 0.148 1.852 15.221
lambda_H[2] 8.479 8.716 0.770 6.037 29.825
lambda_H[3] 6.530 9.949 0.310 3.300 32.218
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 2.838 5.016 0.031 0.985 17.519
lambda_H[6] 5.810 12.345 0.007 0.561 40.298
lambda_H[7] 0.013 0.009 0.002 0.011 0.035
lambda_H[8] 7.631 10.142 0.004 4.258 34.324
lambda_H[9] 0.015 0.010 0.003 0.013 0.040
lambda_H[10] 0.313 1.635 0.032 0.193 0.997
lambda_H[11] 0.278 0.466 0.012 0.129 1.325
lambda_H[12] 4.929 6.302 0.186 2.882 22.230
lambda_H[13] 3.649 3.306 0.265 2.701 12.688
lambda_H[14] 3.303 4.077 0.216 2.031 14.323
lambda_H[15] 0.025 0.044 0.003 0.016 0.088
lambda_H[16] 1.099 2.309 0.043 0.471 5.486
mu_lambda_H[1] 4.405 1.912 1.245 4.229 8.610
mu_lambda_H[2] 3.732 1.933 0.599 3.561 7.832
mu_lambda_H[3] 3.578 1.855 0.795 3.301 7.755
sigma_lambda_H[1] 8.844 4.348 2.096 8.231 18.268
sigma_lambda_H[2] 8.116 4.590 1.009 7.495 18.156
sigma_lambda_H[3] 6.403 4.018 1.056 5.547 16.375
beta_H[1,1] 6.909 1.040 4.340 7.078 8.503
beta_H[2,1] 9.878 0.488 8.846 9.893 10.764
beta_H[3,1] 8.009 0.748 6.206 8.103 9.191
beta_H[4,1] 9.207 7.704 -6.465 9.177 24.034
beta_H[5,1] 0.034 2.389 -4.924 0.190 4.043
beta_H[6,1] 2.936 4.134 -7.302 4.433 7.601
beta_H[7,1] 0.522 5.833 -12.104 0.980 10.660
beta_H[8,1] 2.136 7.116 -2.554 1.230 24.317
beta_H[9,1] 12.972 5.642 1.756 12.943 24.529
beta_H[10,1] 7.070 1.696 3.471 7.161 10.304
beta_H[11,1] 5.166 3.498 -2.674 5.936 9.951
beta_H[12,1] 2.616 1.024 0.884 2.535 4.885
beta_H[13,1] 9.054 0.930 7.187 9.106 10.517
beta_H[14,1] 2.199 1.025 0.262 2.181 4.264
beta_H[15,1] -6.127 3.786 -12.974 -6.268 1.962
beta_H[16,1] 3.481 2.532 -0.772 3.214 9.390
beta_H[1,2] 7.908 0.243 7.405 7.918 8.366
beta_H[2,2] 10.030 0.137 9.764 10.029 10.304
beta_H[3,2] 8.952 0.194 8.569 8.955 9.349
beta_H[4,2] 3.584 1.501 0.760 3.548 6.644
beta_H[5,2] 1.932 0.938 0.068 1.945 3.668
beta_H[6,2] 5.744 1.060 3.298 5.939 7.362
beta_H[7,2] 2.651 1.104 0.714 2.593 5.008
beta_H[8,2] 2.785 1.778 -3.619 3.100 4.231
beta_H[9,2] 3.487 1.114 1.394 3.442 5.835
beta_H[10,2] 8.188 0.345 7.480 8.204 8.834
beta_H[11,2] 9.760 0.627 8.810 9.646 11.172
beta_H[12,2] 3.950 0.377 3.232 3.924 4.739
beta_H[13,2] 9.136 0.249 8.697 9.125 9.613
beta_H[14,2] 4.023 0.347 3.364 4.017 4.690
beta_H[15,2] 11.360 0.687 9.938 11.378 12.708
beta_H[16,2] 4.612 0.821 3.121 4.584 6.292
beta_H[1,3] 8.459 0.238 8.039 8.448 8.977
beta_H[2,3] 10.073 0.116 9.837 10.073 10.302
beta_H[3,3] 9.625 0.164 9.314 9.622 9.963
beta_H[4,3] -2.483 0.903 -4.300 -2.474 -0.708
beta_H[5,3] 3.854 0.628 2.560 3.873 5.064
beta_H[6,3] 8.067 1.198 6.405 7.715 10.699
beta_H[7,3] -2.789 0.654 -4.081 -2.774 -1.512
beta_H[8,3] 5.334 0.805 4.654 5.189 7.969
beta_H[9,3] -2.810 0.743 -4.293 -2.813 -1.402
beta_H[10,3] 8.693 0.284 8.157 8.687 9.277
beta_H[11,3] 8.544 0.288 7.920 8.567 9.057
beta_H[12,3] 5.259 0.319 4.476 5.303 5.775
beta_H[13,3] 8.869 0.177 8.505 8.871 9.204
beta_H[14,3] 5.719 0.276 5.122 5.738 6.206
beta_H[15,3] 10.365 0.318 9.743 10.365 10.984
beta_H[16,3] 6.329 0.641 5.032 6.358 7.560
beta_H[1,4] 8.268 0.171 7.891 8.280 8.571
beta_H[2,4] 10.139 0.116 9.884 10.148 10.345
beta_H[3,4] 10.128 0.158 9.789 10.141 10.406
beta_H[4,4] 11.796 0.458 10.868 11.811 12.681
beta_H[5,4] 5.547 0.785 4.279 5.453 7.372
beta_H[6,4] 7.036 0.939 4.958 7.291 8.382
beta_H[7,4] 8.278 0.350 7.600 8.275 8.954
beta_H[8,4] 6.682 0.333 5.761 6.717 7.128
beta_H[9,4] 7.197 0.462 6.277 7.201 8.113
beta_H[10,4] 7.722 0.234 7.298 7.713 8.198
beta_H[11,4] 9.395 0.203 8.993 9.397 9.788
beta_H[12,4] 7.144 0.212 6.730 7.143 7.592
beta_H[13,4] 9.077 0.145 8.796 9.079 9.361
beta_H[14,4] 7.735 0.224 7.298 7.731 8.205
beta_H[15,4] 9.469 0.239 8.997 9.471 9.947
beta_H[16,4] 9.346 0.246 8.904 9.332 9.859
beta_H[1,5] 8.988 0.146 8.695 8.992 9.266
beta_H[2,5] 10.785 0.093 10.610 10.784 10.978
beta_H[3,5] 10.913 0.170 10.602 10.906 11.262
beta_H[4,5] 8.391 0.472 7.505 8.387 9.386
beta_H[5,5] 5.404 0.599 4.009 5.465 6.433
beta_H[6,5] 8.879 0.633 7.922 8.741 10.392
beta_H[7,5] 6.744 0.334 6.087 6.738 7.439
beta_H[8,5] 8.244 0.291 7.855 8.209 8.954
beta_H[9,5] 8.217 0.476 7.257 8.219 9.154
beta_H[10,5] 10.099 0.230 9.643 10.097 10.539
beta_H[11,5] 11.504 0.234 11.033 11.506 11.967
beta_H[12,5] 8.482 0.195 8.110 8.484 8.882
beta_H[13,5] 10.029 0.131 9.764 10.032 10.285
beta_H[14,5] 9.201 0.233 8.776 9.192 9.688
beta_H[15,5] 11.158 0.253 10.660 11.163 11.638
beta_H[16,5] 9.932 0.174 9.586 9.933 10.272
beta_H[1,6] 10.184 0.190 9.865 10.167 10.614
beta_H[2,6] 11.514 0.106 11.309 11.514 11.726
beta_H[3,6] 10.820 0.162 10.448 10.833 11.108
beta_H[4,6] 12.886 0.819 11.226 12.896 14.404
beta_H[5,6] 5.889 0.603 4.776 5.867 7.106
beta_H[6,6] 8.840 0.673 7.023 8.975 9.818
beta_H[7,6] 9.869 0.563 8.786 9.883 10.949
beta_H[8,6] 9.487 0.398 8.592 9.532 9.964
beta_H[9,6] 8.461 0.793 6.918 8.443 10.091
beta_H[10,6] 9.498 0.325 8.778 9.524 10.075
beta_H[11,6] 10.816 0.354 10.073 10.839 11.467
beta_H[12,6] 9.379 0.253 8.906 9.364 9.907
beta_H[13,6] 11.058 0.164 10.772 11.051 11.391
beta_H[14,6] 9.831 0.293 9.247 9.836 10.400
beta_H[15,6] 10.843 0.434 10.026 10.835 11.681
beta_H[16,6] 10.553 0.239 10.028 10.567 10.996
beta_H[1,7] 10.874 0.871 8.738 10.976 12.285
beta_H[2,7] 12.228 0.427 11.361 12.238 13.073
beta_H[3,7] 10.586 0.666 9.128 10.641 11.697
beta_H[4,7] 2.441 4.136 -5.409 2.356 10.891
beta_H[5,7] 6.391 1.835 2.908 6.326 10.589
beta_H[6,7] 9.670 2.473 4.797 9.596 16.116
beta_H[7,7] 10.484 2.844 5.077 10.372 16.218
beta_H[8,7] 11.103 1.646 9.403 10.905 14.715
beta_H[9,7] 4.492 4.027 -3.436 4.485 12.317
beta_H[10,7] 9.868 1.471 7.196 9.770 13.002
beta_H[11,7] 10.975 1.714 7.702 10.906 14.601
beta_H[12,7] 10.019 0.921 7.994 10.071 11.626
beta_H[13,7] 11.662 0.748 9.755 11.760 12.817
beta_H[14,7] 10.425 0.963 8.493 10.470 12.152
beta_H[15,7] 11.960 2.225 7.510 11.979 16.321
beta_H[16,7] 12.269 1.276 10.262 12.059 15.242
beta0_H[1] 9.034 12.794 -16.057 8.804 37.633
beta0_H[2] 10.704 6.576 -2.002 10.643 23.539
beta0_H[3] 9.923 9.689 -9.999 9.922 29.662
beta0_H[4] 5.651 183.834 -371.519 3.827 410.982
beta0_H[5] 3.738 24.911 -48.940 4.024 52.591
beta0_H[6] 5.557 56.250 -115.807 7.579 120.189
beta0_H[7] 6.400 138.943 -277.941 6.761 280.044
beta0_H[8] 7.023 59.519 -24.833 6.500 36.524
beta0_H[9] 3.237 119.197 -232.133 4.171 239.711
beta0_H[10] 8.491 33.541 -60.862 9.566 75.498
beta0_H[11] 9.060 47.454 -92.549 9.104 108.820
beta0_H[12] 6.655 11.537 -15.317 6.653 28.611
beta0_H[13] 10.020 10.276 -10.067 9.985 29.594
beta0_H[14] 7.151 10.919 -14.446 7.083 29.324
beta0_H[15] 9.094 107.446 -218.544 9.841 224.949
beta0_H[16] 8.112 24.496 -43.896 8.309 58.810